The three people identified with the Brazilian variant of Covid-19 were stopped at Dublin Airport and are now in isolation.
HSE Chief Operating Officer Dr Colm Henry told RTE Radio One this morning that the necessary action were taken.
Dr Henry said: "Let me just reassure people, all the while that was happening, the essential public health measures were taking place, the identifying of contacts, observation and testing of close contacts in these particular cases.
“In these cases, as with any countries of concern, the necessary actions took place from the moment those people arrived in Ireland."
The National Public Health Emergency team announced on Friday night that all three cases are directly associated with foreign travel.
There is "currently no microbiological or epidemiological evidence" that the P1 variant – which was first identified in South America – has had any change in its transmissibility levels.
But Dr Ronan Glynn warned anyone who has travelled from Brazil to quarantine at home for 14 days – and arrange a free Covid-19 test.
The P1 variant has previously been detected in France, Germany, Italy, the Netherlands and Spain.
The announcement comes after NPHET last night confirmed another 763 cases of Covid-19 in Ireland, as well as 28 more deaths.
The figures bring to 213,400 the total number of recorded cases of coronavirus in Ireland.
Tragically, some 4,109 people have now lost their lives as a consequence of Covid-19 since the pandemic hit our shores last spring.
